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Free parallel line calculator - find the equation of a parallel line step-by-step
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Parallel Lines. Parallel lines are straight lines that run in the same direction and are always the same distance apart, ensuring they never meet, no matter how long they are extended. In terms of slopes, two lines are parallel if they have the same slope but different y-intercepts. The formula for slopes in this case is the following: $$ m_1=m ...
Jan 18, 2024 · Let's assume it is (1,6). In other words, x₀ = 1 and y₀ = 6. Write down the equation of your new line: y = ax + b. You will try to determine the values of coefficients a and b. Coefficient a is equal to m. Hence, a = m = 3. Plug the coordinates of point P into the equation of your new line to determine b: y₀ = ax₀ + b. 6 = 3 × 1 + b. b ...
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Two lines are perpendicular when they meet at a right angle (90°). To find a perpendicular slope: In other words the negative reciprocal
When we multiply a slope m by its perpendicular slope −1m we get simply −1. So to quickly check if two lines are perpendicular: Like this:
The previous methods work nicely except for a vertical line: In this case the gradient is undefined (as we cannot divide by 0): m = yA − yBxA − xB = 4 − 12 − 2 = 30= undefined So just rely on the fact that: 1. a vertical line is parallel to another vertical line. 2. a vertical line is perpendicular to a horizontal line (and vice versa).
parallel lines: sameslopeperpendicular lines: negative reciprocalslope (−1/m)- Slope
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For line p, y = m 1 x + b 1, and for line q, y = m 2 x + b 2. If p and q a re distinct (different) lines, they will not coincide (be the same line). This means that b 1 cannot be the same as b 2 because if they are, the lines will be the exact same line.
Sep 2, 2024 · Through the point \((6, −1)\) we found a parallel line, \(y=\frac{1}{2}x−4\), shown dashed. Notice that the slope is the same as the given line, but the \(y\)-intercept is different. If we keep in mind the geometric interpretation, then it will be easier to remember the process needed to solve the problem.
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Example 1: What is the slope of a line parallel to y = 2x + 3, and is passing through (-1, 2)? Solution: The given equation of a line is y = 2x + 3. Comparing this with the slope-intercept form of the equation of line y = mx + c, we have m = 2. The required slope of the parallel line is equal to the slope of this given line and is equal to 2.
